Papers › Differentiating Through Integer Linear Programs with Quadratic Regularization and...
Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splitting
Daniel Mckenzie, Samy Wu Fung, Howard Heaton
In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters w are not directly observed; only contextual data d that correlates with w is available. It is tempting to use a neural network to predict w given d. However, training such a model requires reconciling the discrete nature of combinatorial optimization with the gradient-based frameworks used to train neural networks. We study the case where the problem in question is an Integer Linear Program (ILP). We propose applying a three-operator splitting technique, also known as Davis-Yin splitting (DYS), to the quadratically regularized continuous relaxation of the ILP. We prove that the resulting scheme is compatible with the recently introduced Jacobian-free backpropagation (JFB). Our experiments on two representative ILPs: the shortest path problem and the knapsack problem, demonstrate that this combination-DYS on the forward pass, JFB on the backward pass-yields a scheme which scales more effectively to high-dimensional problems than existing schemes. All code associated with this paper is available at github.com/mines-opt-ml/fpo-dys.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections